# It's some girls' idea of fun -- math camp: 4 area teens bone up for contest in China

- August 06, 2007
- Jill Tucker, Chronicle Staff Writer
- SAN FRANCISCO CHRONICLE
- http://www.msri.org/communications/articles/attachments/mathcampfinal.pdf

**See the article and photograph at the URL above:**

Colleen Lee is at summer camp.

But the 16-year-old isn't making lanyard key chains or tie-dyed T-shirts, or paddling a canoe.

Instead, she's working with algebraic inequalities, applying x2>=0, playing around with symmedians, solving locus problems and learning interesting facts about the triangle.

Lee's in Dallas - yep, Texas - in the summer. At math camp.

That might not sound like a good time to most teenagers, but the Palo Alto High School incoming senior is in training.

She is one of four Bay Area girls heading to China today to participate in the China Girls Mathematical Olympiad, the first time a U.S. team will participate in the annual event.

Marianna Mao of Fremont, Wendy Mu of Saratoga and Patricia Li of San Jose are also on her team.

A four-girl U.S. team from the East Coast will also compete in the event, which runs Aug. 11-17. About 180 girls on 45 teams from several countries will participate.

During the Olympiad, each girl will try to solve four questions in four hours, each of two days.

But these aren't your typical high school calculus kind of problems. They are more like puzzles that require a deep grasp of the theories and concepts that make up the idea of math.

For example: Is it possible to take the numbers 1 through 11 and put them in some order such that 1 plus the first number is a square number, 2 plus second number square number, 3 plus third number is a square, and so on down the line?

While the answer is either a simple yes or no, the participants have to prove their answer.

For the particular question posed above, the answer is no, according to Alison Miller, 21, who is coaching the girls at the Dallas camp, called AwesomeMath.

And we'll trust her on that because she's a Harvard University math major and a 2004 International Mathematical Olympiad gold medalist.

Miller is helping the girls unravel math puzzles using simple techniques like the pigeonhole principle - the idea that if you have more pigeons than holes, you have to put more than one pigeon in a hole.

That doesn't sound like much of a mathematical theory, but the idea can be used to solve even the most complicated problems involving inequalities or, say, infinite sets.

Lee said the days can be long at math camp, with algebraic inequalities and geometry and number theory for hours at a time.

"I won't deny that there are times that I'm bored," she said.

Yet, she said she loves math competitions, qualifying for the trip to Wuhan, China, based on her scores at the USA Mathematical Olympiad.

"It's really satisfying when you can look at a problem and kind of work with it a bit and find a solution for it," she said.

The girls stressed that they aren't doing math the entire time. There's also time for swimming and other organized activities with the many other math students from across the country participating in the camp.

The two U.S. teams competing in China are sponsored by Berkeley's **Mathematical Sciences Research Institute**.

"This is clearly the biggest and the best math event for female high school students in the world," said Zuming Feng of Phillips Exeter Academy, one of three U.S. coaches heading to China with the girls.

Mao, 15, an incoming junior at Fremont's Mission San Jose High School, said Friday she's "pretty excited and also kind of tired."

"I guess we're under pressure, but I'm not too scared or worried about it," she said.

The girls said they can now solve problems they probably couldn't before arriving in Texas.

Algebraic inequalities might be a snap for them, but both Mao and Lee struggled to describe why they like math when others find even simple calculations like balancing a checkbook to be such drudgery.

"There's a large difference between a lot of math classes, where they have to teach you a lot of rules, and these contests," Lee said. "There's more to math than just saying, 'Here's a formula, here's a diagram, plug it in and you're done.' "

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Sample problems

Here are a couple of examples of the kinds of problems the teams will face at the China Girls Mathematical Olympiad:

-- Let ABC be an obtuse triangle inscribed in a circle of radius 1. Prove that triangle ABC can be covered by an isosceles right triangle with hypotenuse square root(2) + 1.

-- An integer is called good if it can be written as the sum of three cubes of positive integers. Prove that for every i = 0;1; 2; 3, there are infinitely many positive integers n such that there are exactly i good numbers among n; n + 2, and n + 28.

This article appeared on page D - 1 of the *San Francisco Chronicle*